## Security and entanglement in differential-phase-shift quantum key distribution.

##### Abstract

Quantum key distribution (QKD) aims at the creation of a secret key in the
two locations of partners, traditionally Alice and Bob, wishing to communicate
in private. A generic QKD protocol utilises a quantum channel and an
authenticated classical channel for exchanges between partners in Phases 1
and 2 of the protocol, respectively. Phase 1 can be described as a prepareand-
measure (P&M) or equivalently as an entanglement-based (EB) phase.
Bob performs the same measurement in both descriptions. Subsequent to
measurement, Phase 2 is commenced, the aim of which is to distill a secret
key from the measurement outcomes resulting from Phase 1.
A necessary condition for the security of a QKD protocol is that the measurement
performed by Bob in Phase 1 must be described by non-commuting
POVM elements. One method of proving the unconditional security of a
QKD protocol is to show that the complete protocol (including Phases 1 and
2) is equivalent to an entanglement distillation protocol. A rst step towards
showing such an equivalence for a given P&M QKD protocol is to describe an
EB translation of Phase 1, where the condition on Bob's measurement is met.
Di erential-phase-shift (DPS) QKD is a member of the class of distributedphase-
reference QKD protocols. Unconditional security proofs for this class
of protocols do not yet exist. Phase 1 of DPSQKD is here described and
formalised as both a P&M and an EB phase, and Bob's measurement is
shown to be described by non-commuting POVM elements. This description
of an equivalent EB translation of DPSQKD where the condition on Bob's
measurement is met, is a fi rst step towards a potential unconditional security
proof for the protocol based on entanglement distillation.